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Author : Patrick Shanahan
Publisher :
ISBN 13 :
Total Pages : 92 pages
Book Rating : 4.:/5 (19 download)
Download or read book The Heat Equation and the Index Theorem -- Expository Comments written by Patrick Shanahan and published by . This book was released on 1988* with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Yanlin Yu
Publisher : World Scientific Publishing Company Incorporated
ISBN 13 : 9789810246105
Total Pages : 287 pages
Book Rating : 4.2/5 (461 download)
Download or read book The Index Theorem and the Heat Equation Method written by Yanlin Yu and published by World Scientific Publishing Company Incorporated. This book was released on 2001 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a self-contained representation of the local version of the Atiyah-Singer index theorem. It contains proofs of the Hodge theorem, the local index theorems for the Dirac operator and some first order geometric elliptic operators by using the heat equation method. The proofs are up to the standard of pure mathematics. In addition, a Chern root algorithm is introduced for proving the local index theorems, and it seems to be as efficient as other methods.
Author : Peter B. Gilkey
Publisher : Publish or Perish
ISBN 13 :
Total Pages : 134 pages
Book Rating : 4.F/5 ( download)
Download or read book The Index Theorem and the Heat Equation written by Peter B. Gilkey and published by Publish or Perish. This book was released on 1974 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Peter E. Gilkey
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (472 download)
Download or read book The Index Theorem and the Heat Equation written by Peter E. Gilkey and published by . This book was released on 1974 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Peter B. Gilkey
Publisher :
ISBN 13 :
Total Pages : 125 pages
Book Rating : 4.:/5 (488 download)
Download or read book The Index Theorem and the Heat Equations written by Peter B. Gilkey and published by . This book was released on 1974 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Yilmaz Akyildiz
Publisher :
ISBN 13 :
Total Pages : 158 pages
Book Rating : 4.0/5 ( download)
Download or read book Expository Lectures on Topology Geometry and Gauge Theories written by Yilmaz Akyildiz and published by . This book was released on 1983 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 1108 pages
Book Rating : 4.3/5 (91 download)
Download or read book Mathematical Reviews written by and published by . This book was released on 2005-06 with total page 1108 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 654 pages
Book Rating : 4.4/5 (91 download)
Download or read book Bulletin of the American Mathematical Society written by and published by . This book was released on 1986 with total page 654 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Peter B. Gilkey
Publisher : CRC Press
ISBN 13 : 9780849378744
Total Pages : 534 pages
Book Rating : 4.3/5 (787 download)
Download or read book Invariance Theory written by Peter B. Gilkey and published by CRC Press. This book was released on 1994-12-22 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book treats the Atiyah-Singer index theorem using the heat equation, which gives a local formula for the index of any elliptic complex. Heat equation methods are also used to discuss Lefschetz fixed point formulas, the Gauss-Bonnet theorem for a manifold with smooth boundary, and the geometrical theorem for a manifold with smooth boundary. The author uses invariance theory to identify the integrand of the index theorem for classical elliptic complexes with the invariants of the heat equation.
Author :
Publisher :
ISBN 13 :
Total Pages : 1608 pages
Book Rating : 4.3/5 (91 download)
Download or read book Subject Guide to Books in Print written by and published by . This book was released on 1983 with total page 1608 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Paul J. Nahin
Publisher : Princeton University Press
ISBN 13 : 0691191727
Total Pages : 232 pages
Book Rating : 4.6/5 (911 download)
Download or read book Hot Molecules, Cold Electrons written by Paul J. Nahin and published by Princeton University Press. This book was released on 2020-03-17 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book is a testament to the intimate, mutual embrace of mathematics and physics. It achieves that by telling the story of an historical event of tremendous impact upon society, both spiritually and technically - the mid-19th century construction of the trans-Atlantic telegraph cable, which reduced the time to send a message across the ocean from weeks to minutes. The story of the cable actually begins decades earlier, at the start of the century, with the French mathematical physicist Joseph Fourier's development of the mathematics that the Scottish physicist William Thomson (later Lord Kelvin) would use to analyze the electrical physics of the cable. The story of Fourier opens the book, that of Thomson completes it, and in-between the reader will learn how to derive Fourier's second-order partial differential equation for the flow of heat energy in matter, how Fourier solved the heat equation, how Thomson used Fourier's solutions to calculate the age of the Earth (imagined to be the result of the of an initially molten sphere of blinding brilliance) and, finally, how Thomson showed that the heat equation also describes the Atlantic cable. An epilogue describing the post-Thomson developments completes the book. All readers who have completed first courses at the level of AP-calculus and AP-physics will be able to read this book. This is a perhaps surprising feature of the book, as the mathematics discussed is normally not encountered until the second year (or even later) of college-level work. This book shows that, in fact, the technical material is fully graspable by a college freshman. Unlike a pure technical book, readers will also find a lot of fascinating history in this book (including the bizarre story of how the English novelist Charles Dickens used the Atlantic cable to send a coded message - during his 1867 American reading tour - to avoid a career-damaging scandal concerning his mistress)"--
Author : Jean-François Le Gall
Publisher : Springer
ISBN 13 : 3319310895
Total Pages : 282 pages
Book Rating : 4.3/5 (193 download)
Download or read book Brownian Motion, Martingales, and Stochastic Calculus written by Jean-François Le Gall and published by Springer. This book was released on 2016-04-28 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô’s formula, the optional stopping theorem and Girsanov’s theorem, are treated in detail alongside many illustrative examples. The book also contains an introduction to Markov processes, with applications to solutions of stochastic differential equations and to connections between Brownian motion and partial differential equations. The theory of local times of semimartingales is discussed in the last chapter. Since its invention by Itô, stochastic calculus has proven to be one of the most important techniques of modern probability theory, and has been used in the most recent theoretical advances as well as in applications to other fields such as mathematical finance. Brownian Motion, Martingales, and Stochastic Calculus provides a strong theoretical background to the reader interested in such developments. Beginning graduate or advanced undergraduate students will benefit from this detailed approach to an essential area of probability theory. The emphasis is on concise and efficient presentation, without any concession to mathematical rigor. The material has been taught by the author for several years in graduate courses at two of the most prestigious French universities. The fact that proofs are given with full details makes the book particularly suitable for self-study. The numerous exercises help the reader to get acquainted with the tools of stochastic calculus.
Author : Ben Andrews
Publisher : Springer Science & Business Media
ISBN 13 : 3642162851
Total Pages : 306 pages
Book Rating : 4.6/5 (421 download)
Download or read book The Ricci Flow in Riemannian Geometry written by Ben Andrews and published by Springer Science & Business Media. This book was released on 2011 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on Hamilton's Ricci flow, beginning with a detailed discussion of the required aspects of differential geometry, progressing through existence and regularity theory, compactness theorems for Riemannian manifolds, and Perelman's noncollapsing results, and culminating in a detailed analysis of the evolution of curvature, where recent breakthroughs of Böhm and Wilking and Brendle and Schoen have led to a proof of the differentiable 1/4-pinching sphere theorem.
Author : Terence Tao
Publisher : American Mathematical Soc.
ISBN 13 : 0821848836
Total Pages : 306 pages
Book Rating : 4.8/5 (218 download)
Download or read book Poincare's Legacies, Part I written by Terence Tao and published by American Mathematical Soc.. This book was released on 2009 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focuses on ergodic theory, combinatorics, and number theory. This book discusses a variety of topics, ranging from developments in additive prime number theory to expository articles on individual mathematical topics such as the law of large numbers and the Lucas-Lehmer test for Mersenne primes.
Author :
Publisher : Academic Press
ISBN 13 : 008095636X
Total Pages : 343 pages
Book Rating : 4.0/5 (89 download)
Download or read book Singular and Degenerate Cauchy Problems written by and published by Academic Press. This book was released on 1977-01-13 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering
Author : John Willard Milnor
Publisher :
ISBN 13 :
Total Pages : 326 pages
Book Rating : 4.3/5 (91 download)
Download or read book The Theory of Characteristic Classes written by John Willard Milnor and published by . This book was released on 1959 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : D.D. Bleecker
Publisher : Springer Science & Business Media
ISBN 13 : 1468406272
Total Pages : 467 pages
Book Rating : 4.4/5 (684 download)
Download or read book Topology and Analysis written by D.D. Bleecker and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Motivation. With intensified use of mathematical ideas, the methods and techniques of the various sciences and those for the solution of practical problems demand of the mathematician not only greater readi ness for extra-mathematical applications but also more comprehensive orientations within mathematics. In applications, it is frequently less important to draw the most far-reaching conclusions from a single mathe matical idea than to cover a subject or problem area tentatively by a proper "variety" of mathematical theories. To do this the mathematician must be familiar with the shared as weIl as specific features of differ ent mathematical approaches, and must have experience with their inter connections. The Atiyah-Singer Index Formula, "one of the deepest and hardest results in mathematics", "probably has wider ramifications in topology and analysis than any other single result" (F. Hirzebruch) and offers perhaps a particularly fitting example for such an introduction to "Mathematics": In spi te of i ts difficulty and immensely rich interrela tions, the realm of the Index Formula can be delimited, and thus its ideas and methods can be made accessible to students in their middle * semesters. In fact, the Atiyah-Singer Index Formula has become progressively "easier" and "more transparent" over the years. The discovery of deeper and more comprehensive applications (see Chapter 111. 4) brought with it, not only a vigorous exploration of its methods particularly in the many facetted and always new presentations of the material by M. F.
